6 research outputs found
Exploring exotic states with twisted boundary conditions
The goal of this thesis is to develop methods to study the nature and properties of exotic hadrons from lattice simulations. The main focus lies in the application of twisted boundary conditions. The thesis consists of a general introduction and the collection of three papers, represented respectively in three chapters. The introduction of the thesis reviews the theoretical background, which is further used in the rest of the thesis. Further, in Chapter 1, implementing partially twisted boundary conditions in the scalar sector of lattice QCD is studied. In Chapter 2, we develop a method to study the content of the exotic hadrons by determining the wave function renormalization constant from lattice simulations, exploiting the dependence of the spectrum on the twisted boundary conditions. Finally, Chapter 3 deals with a novel method to study the multi-channel scattering problem in a finite volume, which is relevant for exotic states. Its key idea is to extract the complex hadron-hadron optical potential, avoiding the difficulties, associated with the solution of the multi-channel Lüscher equation
Partial twisting for scalar mesons
The possibility of imposing partially twisted boundary conditions is
investigated for the scalar sector of lattice QCD. According to the commonly
shared belief, the presence of quark-antiquark annihilation diagrams in the
intermediate state generally hinders the use of the partial twisting. Using
effective field theory techniques in a finite volume, and studying the scalar
sector of QCD with total isospin I=1, we however demonstrate that partial
twisting can still be performed, despite the fact that annihilation diagrams
are present. The reason for this are delicate cancellations, which emerge due
to the graded symmetry in partially quenched QCD with valence, sea and ghost
quarks. The modified Luescher equation in case of partial twisting is given.Comment: 35 pages, 4 figure
The Optical Potential on the Lattice
The extraction of hadron-hadron scattering parameters from lattice data by
using the L\"uscher approach becomes increasingly complicated in the presence
of inelastic channels. We propose a method for the direct extraction of the
complex hadron-hadron optical potential on the lattice, which does not require
the use of the multi-channel L\"uscher formalism. Moreover, this method is
applicable without modifications if some inelastic channels contain three or
more particles.Comment: 26 pages, 12 figure
Generating functional for mesonic ChPT with virtual photons in a general covariant gauge
The divergent part of the one-loop effective action in Chiral Perturbation Theory with virtual photons has been evaluated in an arbitrary covariant gauge. The differential operator that emerges in the functional determinant is of non-minimal type, for which the standard heat kernel methods are not directly applicable. Both the SU(2) and SU(3) cases have been worked out. A comparison with existing results in the literature is given